Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. ABSTRACTHough has proposed an interesting and computationally efficient procedure for detecting lines in pictures. In this paper we point out that the use of angle-radius rather than s lope-intercept parameters simplifies the computation further. We also show how the method can be used for more general curve fi tting, and give alternative interpretations that explain the source of its efficiency.

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The head-related transfer function ͑HRTF͒ varies with range as well as with azimuth and elevation. To better understand its close-range behavior, a theoretical and experimental investigation of the HRTF for an ideal rigid sphere was performed. An algorithm was developed for computing the variation in sound pressure at the surface of the sphere as a function of direction and range to the sound source. The impulse response was also measured experimentally. The results may be summarized as follows. First, the experimental measurements were in close agreement with the theoretical solution. Second, the variation of low-frequency interaural level difference with range is significant for ranges smaller than about five times the sphere radius. Third, the impulse response reveals the source of the ripples observed in the magnitude response, and provides direct evidence that the interaural time difference is not a strong function of range. Fourth, the time delay is well approximated by well-known ray-tracing formula due to Woodworth and Schlosberg. Finally, except for this time delay, the HRTF for the ideal sphere appears to be minimum-phase, permitting exact recovery of the impulse response from the magnitude response in the frequency domain. a radius of the sphere ͑m͒ c ambient speed of sound ͑m/s͒ f frequency ͑Hz͒ h head-related impulse response h m mth-order spherical Hankel function h m Ј the derivative of h m with respect to its argument Hhead-related transfer function relative to free field H head-related transfer function relative to source i ͱϪ1 j m mth-order spherical Bessel function k acoustic wave number ͑/m͒ n m mth-order spherical Neumann function p f f free-field pressure at the center of the sphere ͑kg/m 2 ) p s pressure on the surface of the sphere ͑kg/m 2 ) p pressure at a small sphere surrounding the source ͑kg/m 2 ) P m Legendre polynomial of degree m Q m mth-order modified spherical Hankel function r distance from the center of the sphere to the source ͑m͒ r radius of a small sphere surrounding the source S magnitude of flow from an ideal point source ͑m 3 /s͒ t time ͑s͒ ⌬t time between arrival at observation point and sphere center ͑s͒ ⌬ normalized ⌬t angle of incidence ͑rad͒ 0 angle for tangent incidence ͑rad͒ wavelength ͑m͒ normalized frequency normalized distance to the source 0 density of air ͑kg/m 3 ) normalized time radian frequency ͑rad/s͒